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Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers): 4 x ^1 / 2

11  Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):  4 \sqrt x - 2

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Given

f(x)=4 \sqrt x - 2

It can also be written as 

f(x)=4 x^{\frac{1}{2}} - 2

Now,

As we know, the property,

f'(x^n)=nx^{n-1}

and the property 

\frac{d(y_1+y_2)}{dx}=\frac{dy_1}{dx}+\frac{dy_2}{dx}

applying that property we get

f'(x)=4 (\frac{1}{2})x^{-\frac{1}{2}} - 0

f'(x)=2x^{-\frac{1}{2}}

f'(x)=\frac{2}{\sqrt{x}}

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